Higher order systematic effect in Ptolemy's Geographia coordinate description of Iberia

14 Pages·2008·3.18 MB·English

Angeliki Tsorlini ∗

Higher order systematic effect in Ptolemy’s Geographia
coordinate description of Iberia

Keywords: Ptolemy’s Geographia; Ptolemy’s coordinates; Ptolemaic reference system; best fitting;
spatial distribution of longitude and latitude differences.

Summary
Claudius Ptolemy, in his Geographia describes geographic sites (i.e. towns, mountain
picks, river mouths, promontories and other) as points with given coordinates of
spherical longitude and latitude type. These geographic coordinates are following the
known Ptolemaic reference system of parallels and meridians, the origin of which are
respectively close to actual Equator and close to the Canary Islands many degrees
west of the today’s origin at Greenwich. It is also known that though latitudes is
rather well defined, considering the level of measuring accuracy at Ptolemy’s times,
the longitudes suffer severe shortcomings which are due to the difficulties of
measurement time, which corresponds to the longitude. The longitude values given by
Ptolemy are also strongly dependent upon the distance from the Canaries eastwards.
In the paper, part of a broader research carried out the last years by the Cartography
Group of our Faculty, we focus our interest on Ptolemy’s coordinates given in
Geography for Iberia. Storing digitally the coordinates for the area of interest (almost
520 pairs of coordinates), and snooping the data, which is a laborious process because
it requires the cross-checking with the relevant coordinates given in a number of
Ptolemy’s Geographia editions (in our case there are used four), the finally accepted
list is formed which is compared with their today’s values. The core of the study
concerns a two-dimensional spatial analysis of the field of differences, testing various
transformation functions in order to determine and eliminate the systematic error
pattern inherent in Ptolemy’s coordinates. The result, using new “reductive” methods
in the comparison analysis (e.g. the concepts of the unit sphere, of the common
projective support) with all affined illustrations of the associated test, shows the
pattern of coordinate differences free of systematic effects up to the 2nd order, testing
also and some higher order effects in order to get a better understanding of the whole
process. Finally, a field of various classes of spatial deformations of isotropic and
anisotropic character, is once more, tested and visualized.

Introduction

The interest in the geometric properties of historic maps has never been exhaustively and
continuously treated by analytical means, especially in the modern era of cartography.
The analytical treatment of the geometric background of early maps is an issue that today
attracts the attention it deserves, as a result of the challenging perspectives opened by new
digital technologies. These new technologies offer generously adequate processing tools
that allow diving into the world of the geometric origin and properties of historic carto-
graphic representations and maps.

∗ Surv. Engineer, MSc Carto & Geogr., PhD Cand., Aristotle University of Thessaloniki, Greece.
[[email protected]]
[1]
Previous research showed the order of magnitude of the longitude and latitude differences
of Ptolemy’s values from the today’s counterparts both in broader and local scale
(Livieratos, 2006), diving into a systematic geodetic approach on the issue for the area of
actual Greece (Tsorlini, Livieratos, 2006).
The core of this study concerns a two-dimensional spatial analysis of the field of
differences, testing various transformation functions in order to determine and eliminate
the systematic error pattern, inherent in Ptolemy’s coordinates for the biggest part of
Iberian Peninsula. The result, using ‘reduction’ methods in the comparison analysis (e.g.
the concepts of the unit sphere, of the common projective support) with all affined
illustrations of the associated test, shows the pattern of coordinate differences free of
systematic effects up to the second order.

Ptolemaic reference system and coordinates

Ptolemy, in his Geographia, gives a list of geographic coordinates of spherical longitude
and latitude of almost ten thousand of point locations, on the earth surface, as known at
his times. These points are referred to geographic sites (i.e. towns, mountain picks,
river mouths, promontories and other) and their geographic coordinates are following the
known Ptolemaic reference system of parallels and meridians, the origin of which is
respectively close to actual Equator and close to the Canary Islands almost 18 degrees
west of the today’s origin at Greenwich (Figure 1).

Figure 1. The origin of parallels and meridians in Ptolemy’s Geographia.
[2]
Coordinates in Ptolemy’s Geographia

The world of Ptolemy is classified in Regions, since each chapter is referred to one of
them, giving by this way the Atlas concept. The smaller the table is the more important
and detailed the region appears to be in Ptolemy’s Geographia, as it is obvious from the
next Figure (Figure 2).

Figure 2. The ‘Tabulae’ in Ptolemy’s Geographia.

Figure 3. Table II in Ptolemy’s Geographia and the regions of Hispania depicted on it.
[3]
In this paper, which is a part of a broader research carried out the last years by the
Cartography Group in the Faculty of Surveying Engineering at Thessaloniki, we focus our
interest on Ptolemy’s coordinates given in Geographia for Hispania listed in Book II,
Chapters III to V and depicted in Table II of Europe. There are three regions in Iberia,
which are Hispania Baetica, Hispania Lusitania and Hispania Tarraconensis, and they are
depicted in Figure 3.
In this case, we are talking about almost 520 pairs of coordinates, from which almost 470
refer to the actual territory of Spain. The editions, we use for this particular study are the
following four:
a. the Vatopedion Codex (13th -14th century),
b. the Marciana Codex (15th century),
c. the Donnus Nicolaus Germanus mid-15th century manuscript of Ptolemy’s Geo-
graphia as given in Codex Ebnerianus (Stevenson 1991: 92) and
d. the printed edition of Ptolemaios, Handbuch der Geographie by A.
Stueckelberger -G. Grasshof, Basel, 2006

Processing the Ptolemy’s Coordinates

According to the procedure we follow, we first collect the coordinates of the area of
interest from the different editions of Ptolemy’s Geographia we have, we transcribe them
from Byzantine writing, if it’s necessary, and then, we store them digitally in a database
(Table 1), having by this way the digital cataloguing of geographic coordinates.

Table 1. A part of the database showing the coordinates in all the editions used for this study.

The coordinates from the four sources, are independently and mutually checked and
evaluated through this database, in order to detect discrepancies in the point placement,
gross errors, double values an edition may have for the same toponym, or lack of values
and toponyms in some editions (Table 2).
[4]
Table 2. Lack of toponyms in the editions.

The next step is the projection of the toponyms onto a map with a relevant graticule of
parallels and meridians, all of them plotted in the same projection, e.g the elementary
geographic projection (y = Rφ,x= Rλ), assuming a unit radius reference sphere (R =1)
for the earth’s model. In this process, maps are plotted from the coordinates and by this
way, the locations of points are visualized, making easier the auto- and cross- checking of
the values, the detection of the differences, the gross errors, the double values and other
displacements they may occur. The next figures show, as an example, the gross errors in
all editions, as they were detected in the database (Table 3) and visualized, after their
projection on a map (Figure 3).

Table 3. The gross errors in Hispania in the editions used.
[5]
Figure 3. The visualization of gross errors and their correction in each edition.

The projection of toponyms to a map for the editions used in this study, after their
correction from gross errors, is shown in the images below (Figure 4). The initial letter in
the right corner of each map indicates the edition of Ptolemy’s Geographia, while the
different colors of the points are referred to the different regions as described in
Geographia.

Figure 4. Coordinate plotting in geographic projection according to the snooped list of Ptolemy’s coordinates for
Iberia. The initial letters on the four images indicate the edition of Ptolemy’s Geographia
(G:Germanus’ edition, B: Ptolemaios, Handbuch der Geographie, Basel, 2006, Ma: Marciana Codex and
V:Vatopedion Codex).
[6]
Having projected the coordinates on the map, we compare and analyze them using
geodetic methods, so as to try to conclude to an accepted list without gross errors, double
values or records or other apparently erroneous discrepancies in point placement.

The identification of ancient toponyms with their modern counterparts

Another important procedure in this study is the identification of ancient toponyms with
their modern counterparts. Having concluded to an ‘accepted’ list of coordinates without
gross errors, double values or records or other apparently erroneous discrepancies in point
placement, we start the comparison of Ptolemy’s coordinates with their today’s
counterparts. In order to perform such a comparison and to identify the coincidence of
places in Ptolemy’s era with their today’s counterparts, we had to compare the toponyms
of each area of Ptolemy’s Hispania with the toponyms of the corresponding area of actual
Spain and Portugal, confirming at the end the coincidence of the with certainty known
points in both cases, based mainly on old maps and relevant references in historical and
archeological sources.
In this study, the whole inquiry of maps, old and modern, and of the other historical data,
collected and used for the identification of ancient toponyms with modern, is based on
internet. The criteria used for the selection of the maps are mainly their resolution - the
bigger resolution the map has, the better and easier it can be read after its fitting to the
graticule, plotted for the area of interest - and the existence of geographic graticule on the
map, which helps maps’ fitting to the ‘plotted’ graticule. With regard to old maps, it is
also important to check three more things before the selection of an old map. These are
the prime meridian, the toponyms on the map and the coastline.
In ancient times, there were various conventions for the prime meridian, something that
influences straightly the old maps. Ptolemy used in his Geographia, as prime meridian,
that in Canary Islands. The modern prime meridian is passing through Greenwich. For
this reason, it is important to select a map with the prime meridian in Greenwich, so that
the control points used in the best fitting process can be easily found.

Figure 5. Historical maps with different prime meridian
(a) Hispania antiqua, A.Dell, B.Borghi, Firenze, 1819, (b) Hispania antiqua, Sidney Hall, 1830, (c) Espagne
ancienne / Dressée par A. Villemin ; Lale direct. et scrip, 1800, (d) Hispania et Insule, John Arrowsmith, 1840

[7]
Regarding the toponyms, it is important to find maps with ancient toponyms together with
the modern coastline, because in that way the modern places where the ancient toponyms
are located, can be more easily detected. For this reason, it is important for us to use
maps, where the coastline of Iberian Peninsula and of the islands around it, is similar to
the modern one, so that it can be fitted exactly to the modern map. The next figures show
examples of these two last cases (Figure 6-7).

Figure 6. Maps of Spain and Portugal with different toponyms.
The first map (A Map of Spain & Portugal, published in Robert Wilkinson's General Atlas,
circa 1794) has modern toponyms and the other (Hispania et Insule, A. & S. Arrowsmith, 1829) ancient.

(a) (b)
Figure 7. Ancient maps best fitted to the modern. The coastline of Iberian Peninsula in the first map doesn’t fit
well to the modern, while in the second, the coastline fits exactly ((a): Map of Spain and Portugal, C.S. Hammond
& Co., N.Y.,1921, (b): Hispania, Alex Findley, published by T.Tegg, London, 1830)

Based on these criteria, at first, modern maps and then old maps are selected and fitted
with the best possible way to the ‘plotted’ graticule, using as control points, the common
nodes of the graticule. The procedure followed in this case is shown in the figure below
(Figure 8).
The old maps, selected and fitted to the modern map in order to help to the identification
of ancient toponyms with modern are:
a. Hispania antiqua, Sidney Hall, 1830 (Figure 9d)
[8]
Figure 8. The best fitting of modern and old maps to the graticule plotted
in the area of actual Spain and Portugal

Figure 9. Old maps (a) Hispania et Insule, John Arrowsmith, 1840, (b) Hispania, Alex Findley, London, 1830,
(c) Map of Spain, Classical Atlas of Ancient Geography, A. G. Findlay, New York, 1849 (d) Hispania antiqua
S. Hall, 1830 (e) Hispania, Atlas Of Ancient And Classical Geography, J. M. Dent And Sons, 1912
[9]
b. Hispania, Alex Findley, published by T. Tegg, London, 1830 (Figure 9b)
c. Hispania et Insule, John Arrowsmith, 1840 (Figure 9a)
d. Map of Spain from A Classical Atlas of Ancient Geography by Alexander G.
Findlay. New York: Harper and Brothers 1849. (Figure 9c)
e. Hispania-Spain, Atlas Of Ancient And Classical Geography, J. M. Dent And
Sons, 1912 (Figure 9e)
Having compared the toponyms, the ancient with modern, we concluded to have almost
300 identified points, without counting on them the mountains and some physical borders,
Ptolemy included in his Geographia. Most of these points will be used as control points in
best fitting Ptolemy’s map for Hispania to the modern map of Spain and Portugal. In the
next map (Figure 10), we can see on a modern map, the places, where most of Ptolemy’s
toponyms in Iberian Peninsula, are detected according to historical and other sources.

Figure 10. Ptolemy’s toponyms of Hispania depicted on a modern map

Best fitting of Ptolemy’s representation to a modern map

The points, we have mentioned before, have great importance to the continuity of this
work because a set of them, properly distributed to the overall map space, is selected and
brought into one to one correspondence with the actual coordinates of the same set of
points in the modern map, after choosing a transformation system, in this case a 2nd order
polynomial transformation, involving a projection and an earth’s model. The result of the
best fitting of Ptolemy’s coordinates to the modern counterparts is shown in Figure 11.
The Ptolemy representation is georeferenced to actual geographic coordinates using
almost 270 control points properly distributed in the area of Spain and Portugal.
Ptolemy’s graticule, extended from 2˚ to 21˚ in longitude and from 36˚ to 47˚ in latitude,
contrary to the geographic graticule of the modern map, which extended from -10˚ to 5˚
[10 ]